Answers
=======================================================
Work Shown:
We'll apply these log rules
[tex]\text{Log Rule 1: } \ \ \ \ln\left(\frac{x}{y}\right) = \ln(x) - \ln(y)\\\\[/tex]
[tex]\text{Log Rule 2: } \ \ \ \ln\left(x^y\right) = y\ln(x)\\\\[/tex]
These log rules can be used for logs of any base, and not just natural logs.
[tex]z = \ln\left(\frac{\sqrt{x}}{y}\right)\\\\z = \ln\left(\sqrt{x}\right)-\ln\left(y\right) \text{ ... Use log rule 1}\\\\z = \ln\left(x^{1/2}\right)-\ln\left(y\right)\\\\z = \frac{1}{2}\ln\left(x\right)-\ln\left(y\right) \text{ ... Use log rule 2}\\\\z = \frac{1}{2}u-v\\\\[/tex]
Therefore,
[tex]\ln\left(\frac{\sqrt{x}}{y}\right) = \frac{1}{2}u-v\\\\[/tex]
when [tex]u = \ln(x) \ \text{ and } \ v = \ln(y)\\\\[/tex]
Related Questions
Find the area of OP. Leave your answer in terms of .
A. 14 cm2
B. 77 cm2
C. 147 cm2
D. 497 cm2
Answers
Answer:
D. 49
Step-by-step explanation:
The area of a circle is pi times the radius squared (A = pi r^2).
so putting in your numbers given you get 7^2
which equals 49
The area of a square is 144 in.2
What is the length of one side of the square?
Answers
Answer:
12 inches
Step-by-step explanation:
Find the square root
144² ÷ 2 = 12
Therefore, the length of one of the sides of the board with an area of 144 sq. in is 12 inches.
HELP!!!
WHO EVER HELPS ME FIRST GETS BRAINLEST!!!!How can decomposing a parallelogram and composing it as
another shape help in understanding the formula for the area of
a parallelogram?
Answers
What’s the Answer of this question plz? The total
Answers
Answer:
I think it's six
Step-by-step explanation:
A= 1
b= 2
c= 3
Which sentence has the quotation marks placed correctly ?
1.) “Mother ," I cut my finger , said Jane.
2.) "Mother, I cut my finger," said Jane.
3.) Mother, I cut my finger, "said Jane."
4.) "Mother, I cut my finger, said Jane."
Answers
Segments AB and CD coincide.
Vinay concluded: "Segments AB and CD have no angles with the same measurement, so they are not congruent."
What error did Vinay make in his conclusion?
Choose 1 answer:
A. These segments are mapped onto each other, so they are congruent
B. The segments are not congruent, because no transformations were used
C. There is no error. This is a correct conclusion
Answers
Answer:
A
Step-by-step explanation:
The correct reason should be These segments are mapped onto each other, so they are congruent.
What is Congruency.In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
We have the statements as
Segments AB and CD coincide
Now, Vinay concluded: "Segments AB and CD have no angles with the same measurement, so they are not congruent."
As per Vinay the lines would never able to coincide if they are not congruent.
So, the correct reason should be These segments are mapped onto each other, so they are congruent.
Learn more about Congruent here:
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5. Match each description with the correct equation below. Then solve the equation.
a) When 4.26 is added to a number, the sum is 17.04.
b) The product of 4.26 and a number is 17.04.
c) When a number is doubled and 4.26 is subtracted, the result is 17.04.
4.26n = 17.04 2n − 4.26 = 17.04 n + 4.26 = 17.04
Answers
Answer:
.
Step-by-step explanation:
There are 25 pineapples in a basket. Each pineapple weighs 100 grams. What is the total weight off all the pineapples in the basket? Please use complete sentences when answering the question.
Answers
PLEASE HELP ILL DO ANYTHING
Answers
Answer:
i took this test along time ago 3,1,1
The perimeter of a triangle is 64 in. The longest side is 14 in. Longer than the medium side, and the medium side is 7 in. more than the shortest side. Find the length of each side of the triangle
Answers
Answer:
longest side =33
medium side =19
shortest side = 12
Step-by-step explanation:
Let medium side be x
then longest side =14 +x
shortest side = x-7
we know that ,
perimeter =sum of all side
or, 64 = 14+ x + x + x -7
or, 64 - 7 = 3x
or, 57 = 3x
or, 57÷3 = x
or, x = 19
then
medium side =x = 19
longest side =x+14 =33
shortest side = x- 7 = 12 #
An auto assemply worker requires 4 electrical fuses for each vehicle. The supplier of the fuses has informed the plant manager that 5% of all the fuses they produce are defective. Assume that the assembly worker selects the 4 fuses for any vehicle at random and independently of each other. If 2 assembled vehicles are selected at random and independently of one another, what is the probability that both vehicles will have all defective fuses
Answers
Answer:
[tex]3.9 \times 10^{-11}[/tex] probability that both vehicles will have all defective fuses
Step-by-step explanation:
For each fuse, there are only two possible outcomes. Either they are defective, or they are not. The probability of a fuse being defective is independent of any other fuse. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Probability of a vehicle having all defective fuses:
5% of fuses are defective, which means that [tex]p = 0.05[/tex]
A vehicle has 4 fuses, which means that [tex]n = 4[/tex].
This probability is P(X = 4). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.05)^{4}.(0.95)^{0} = 0.00000625[/tex]
If 2 assembled vehicles are selected at random and independently of one another, what is the probability that both vehicles will have all defective fuses?
For each vehicle, 0.00000625 probability of having all defective fuses. For 2:
[tex](0.00000625)^2 = 3.9 \times 10^{-11}[/tex]
[tex]3.9 \times 10^{-11}[/tex] probability that both vehicles will have all defective fuses
of you would Write a decimal that represents the value of one $1 bill and 5 quarters how would you write that?
Answers
This is because 4 quarters equal $1.00. You add another quarter and you get $1.25. Hope this helps!!
Please solve and I will give brainliest!
Answers
Answer:2
0
+
1
0
Step-by-step explanation:
Answer:
question 1: 10 + 20f
question 2: 164,340
Step-by-step explanation:
question 1:
10(1 + 2f)
(10 x 1) + (10 x 2f)
10 + 20f
question 2:
120n + 160,500 n =32
120(32) + 160,500
3,840 + 160,500
164,340
Nationwide Insurance would like to perform a chi-square test to investigate whether a difference exists in the proportion of male and female teenagers who text while they drive. A random sample of 80 male teenagers found that 50 indicated they texted while driving. A random sample of 120 female teenagers found that 65 indicated they texted while driving. The degrees of freedom for the chi-square critical value is ________.
Answers
Answer:
1
Step-by-step explanation:
There are 2 categories male and female and 1 attribute those who text during driving so the number of cells is 2*1= 2
And degrees of freedom is found by subtracting 1 from k= k-1= 2-1= 1 where k is the number of the categories
The degrees of freedom for this chi square test of proportions is 1
The critical value for ∝= 0.05 is .χ²≥ χ²(0.05,1)= 3.84
The critical value for ∝= 0.01 is .χ²≥ χ²(0.05,1)= 2.71
Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 18)(0,18) and (2, 288)(2,288).
Answers
Answer:
[tex]y = 18*4^x[/tex]
Step-by-step explanation:
We want an exponential equation in the following format:
[tex]y = ab^x[/tex]
Point (0,18):
This means that when [tex]x = 0, y = 0[/tex]. So
[tex]y = ab^x[/tex]
[tex]18 = ab^0[/tex]
[tex]a = 18[/tex]
So
[tex]y = 18b^x[/tex]
Point (2,288):
This means that when [tex]x = 2, y = 288[/tex]. So
[tex]y = 18b^x[/tex]
[tex]18b^2 = 288[/tex]
[tex]b^2 = \frac{288}{18}[/tex]
[tex]b^2 = 16[/tex]
[tex]b = 4[/tex].
So
[tex]y = 18*4^x[/tex]
Determine the slope of the line that passes through the points (-4,-2) and (3,1).
Answers
Answer:
Step-by-step explanation:
Stephanie, so many people ask questions about this type of problem, I think the teachers don't know how to explain these at all. Ask your teacher if I can have some of their salary :) I have to explain this to that many people.. :0
given"
point P1 (-4,-2) in the form (x1,y1)
point P2(3,1) in the form (x2,y2)
slope = m
formula for slope is:
m = (y2-y1) / (x2-x1)
m = (1-(-2) ) / (3 - (-4))
m = (1+2) / (3+4)
m = 3 /7
That's your slope, ask if you need more explanation, I'm really curious about why this type of problem causes so many questions :/
HELP HELP 6th grade help
Answers
Answer:
A: numerical
B:catergorical
C:catergorical
Step-by-step explanation:
difference between the place values of 2 is in 4242
Answers
Answer:
[tex]\huge\colorbox{violet}{✏﹏ \: ᴀɴsᴡᴇʀ \: }[/tex]
4242
2 = 200 ( 2 is in hundred's place )
4242
2 = 2 ( one's place )
Difference = ?
[tex] = 200 - 2 \\ = 198[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
Please hel p me. !!!!!!!
Answers
Answer:
7,3921
Step-by-step explanation:
4. What type of line of symmetry does this triangle have? horizontal vertical This triangle has no line of symmetry. diagonal
Answers
I don’t know what to do please don’t give me files I don’t get it
Answers
Answer:
i believe its dependent
Step-by-step explanation:
7x1,000,000,000-5.8x1,000,000,000
Answers
Answer:
1200000000
Step-by-step explanation:
ia had 50 carrot sticks for her
study group to snack on. There were
6 people eating the carrot sticks, and
each person ate an equal number of
carrots until there weren’t enough
left to share equally. How many
carrot sticks were left over? Explain.
Answers
Answer:
8.333333333 or 25 /3
Step-by-step explanation:
HELP ME PLEASE I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!:)
Christa went shopping for back-to-school clothes. Before the tax was added on, her total was $176. If the sales tax is 6%, what was the total amount she paid? A) $10.56 B) $105.60 C) $126.56 D) $186.56
Answers
Answer:
Christa went shopping for back to school clothes.
She paid a total of 176 dollars before the tax was added on.
Now, how much will she be paying if the sales tax is 6% what was the total amount she paid.
Solutions:
=> 176 dollars * 6% to get the amount
=> 6% / 100% = 0.06
=> 176 dollars * .06 = 10.56
Now, let’s add to get the answer
=> 176 dollars + 10.56 dollars = 186.56 dollars
Step-by-step explanation:
MRK ME BRAINLIEST PLZZZZZZZZZZZZ
Answer:
it should be d $186.56
Step-by-step explanation:
this should help you
Find the median and mean of the data. Which reflects the best measure of the center?
43, 38, 37, 57, 57 58, 45
Answers
mean= 47.857
Median: like up the numbers least to greatest and then find the number in the middle. if there is an even number of values, take the average of the two middle values
median= 45
The mean reflects the beet measure of the center.
PLZ HELP IWILL GIVE BRAINLIESTTT
Answers
Answer:
Choice B
A = b x h
Step-by-step explanation:
In other words the area of a parallelogram is the base times height
In a rational function, what must be true for the graph to have a horizontal asymptote at
y = 0.
Answers
Answer:
m = 0
Step-by-step explanation:
Consider the series 7/9+7/27+7/81+1/243 Which expression defines Sn?
Answers
Answer:
It’s d
Step-by-step explanation:
The sum of the series is given by option D.
What is a Geometric Series?A sequence of numbers such that the consecutive term is increasing or decreasing by a fixed ratio is called a geometric series.
The series is
7/9+7/27+7/81+1/243 +.................
The common ratio is
(7/27) / (7/9) = 1/3
r < 1
The sum of the geometric series when r < 1 is given by
Sn = a ( 1-rⁿ)
Sn = [tex]\rm \lim_{n \to \infty}[/tex] (7/9) ( 1- (1/3)ⁿ)
To know more about Geometric Series
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Find the probability of two persons being born on the same day?
Answers
Answer:
1/365
Step-by-step explanation:
The probability of being born any day of the year is 1 or more specifically: 365/365. Since Person B must be born on the same day as Person A their probability is 1/365
Answer:
Person A can be born on any day of the year since they’re the first person we’re asking. The probability of being born any day of the year is 1 or more specifically: 365/365.
Since Person B must be born on the same day as Person A their probability is 1/365.
We want both of these events to happen so multiply the probabilities:
365[tex] \frac{365}{365} . \frac{1}{365} = 0.0027[/tex]So you have a 0.27% chance of walking up to a stranger and discovering that their birthday is the same day as yours.
I think you are happy with this answer
I need help as soon as possible!! Please!!
Answers
Answer:
Option A, (x + 6, y - 4)
Hope this helps!
Answer:
1st option
Step-by-step explanation:
Consider the coordinates of R and R'
R (2, 6 ) and R' (8, 2 )
R → R' in the x- direction is + 6 ( 2 to 8 )
R → R' in the y- direction is - 4 ( 6 to 2 )
Then the translation rule is
(x, y ) → (x + 6, y - 4 )